Naming1

    schema elimE = {
        type t
    relation p(X:t)
        property exists X. p(X)
    fresh individual n:t
    #----------------------
    property p(n)
    }

type t
relation succ(X:t,Y:t)

   axiom exists Y. succ(X,Y)

    function next(X:t):t

    property succ(X,next(X))
    proof
        apply elimE with n = next(X), p(Y) = succ(X,Y)

    property exists Y. succ(X,Y) named next2(X)
definition next2(X) = 0 definition next2(X) = 1